Multipole correlations of -orbital Hubbard model with spin-orbit coupling

Onishi, Hiroaki  

We investigate multipole properties in the ground state of a -orbital Hubbard model with the spin-orbit coupling, by exploiting numerical techniques. Here let us consider a one-dimensional chain along the direction with five electrons per site. Due to the spatial anisotropy of orbitals, and orbitals are active in the absence of the spin-orbit coupling. When the spin-orbit coupling is weak, spin and orbital are independent degrees of freedom at local level. With the increase of the spin-orbit coupling, the total angular momentum turns to give a good quantum state. The spin state changes from an antiferromagnetic state to a ferromagnetic state. Regarding the orbital state, the spin-orbit coupling would lead to a complex orbital state. In the presentation, we will discuss how the spin-orbital state can be understood from the viewpoint of multipole.